Adaptive noise filtering and equalization

ABSTRACT

Processing a signal comprising signal distortions with filters. The filters comprise a first filter configured to a first time scale to compensate for signal distortions within respective symbols of the signal and a second filter configured to a second time scale to compensate for signal distortions among symbols of the signal. A probability estimate is produced based on an output of at least one of the first and second filters. At least one of the first and second time scales is adjusted according to the probability estimate.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation under 35 U.S.C. §120 of U.S.non-provisional patent application Ser. No. 12/583,006, filed on Aug.11, 2009, which is a continuation of U.S. non-provisional patentapplication Ser. No. 11/358,901, filed Feb. 21, 2006, now U.S. Pat. No.7,573,966, which is a continuation of U.S. non-provisional applicationSer. No. 10/620,477, filed Jul. 15, 2003, now U.S. Pat. No. 7,035,361,which claims priority under 35 U.S.C. §119(e) to U.S. provisionalapplication No. 60/396,065. The entire contents of each of theabove-recited patent applications is hereby incorporated herein byreference.

FIELD OF THE INVENTION

The present invention relates to communication systems and improving thereceived signal quality in a high-speed communications environmentthrough the use of equalization. The improvement in signal qualityaffords gains in system performance such as increased data throughputcapacity or reduced error rate. Specifically, the present inventionrelates to a method and system for improving the quality of a receivedsignal by counteracting distortions introduced in signal generation,transmission, and reception.

BACKGROUND OF THE INVENTION

Network bandwidth consumption is rising at a rapid rate. Existingnetwork capacity is marginally adequate and is expected, as of thiswriting, to soon be inadequate. Thus, there is a need to increasenetwork bandwidth capacity. This increase in bandwidth can be achievedby increasing the symbol transmission rate to yield a correspondingincrease in the data rate or by using advanced modulation techniqueswith higher spectral efficiency (i.e. techniques that communicate morethan one information bit per symbol).

Regardless of the technique employed to achieve higher data throughput,the higher data throughput can place more stringent requirements on thefidelity of the signal communicated. Fidelity of the signal communicatedcan be hampered by signal degradation. Signal degradation can occurduring signal generation and signal transmission. Signal degradationincurred in generating and transmitting a signal over a channel canlargely be categorized as arising from two sources: (i) filtering of thesignal and (ii) corruption from noise.

In classical communications (e.g. wireless or wireline communications),the noise component is commonly addressed by using optimal detection(i.e. matched-filtering followed by optimal thresholding). However, sucha conventional approach often neglects the inter-symbol interference(ISI) associated with the filtering that occurs in the channel, i.e.that approach assumes that the noise is the dominant source ofdistortion. If the ISI is the dominant source of signal degradation,then the conventional approach is to equalize the channel, e.g. filterthe received signal with an inverse filter prior to detection. The useof any one of these approaches in isolation may not improve signalfidelity since matched-filtering and equalization are oftencontradicting goals.

For example, equalization generally corresponds to high-pass filteringwhich, while removing ISI, increases the presence of high-frequencynoise. A low-pass filter (LPF) is usually employed to the equalizedsignal in order to reduce the effect of the high-frequency noise butwhich also re-introduces ISI. Matched-filtering, on the other hand, isoften low-pass in nature and thus frequently exacerbates the ISI in thesignal in the process of reducing noise.

The separate application of matched-filtering and equalization can becharacterized as “ad-hoc” because it does not consider the problem ofnoise mitigation and equalization in a combined framework, and thus,neglects the impact each has on the other.

There exist techniques in the conventional art which address noisemitigation and equalization in a common framework. In particular, thewell-known Least-Mean Squares (LMS) based approaches minimize adistortion measure that captures the impact of both noise and ISI.Furthermore, these methods are adaptive in the sense that the settingsof the filter are automatically adjusted to the optimal value. Thisadaptive feature is often necessary as the exact characteristics of thechannel distortion and noise spectral content vary from installation toinstallation and also with time and temperature in some instances.

Unfortunately, the use of these traditional adaptive LMS-based controlmethodologies for high-data rate systems can be impractical due to dataacquisition and processing difficulties. In particular, it can beeconomically impractical (and often technically infeasible) to (i)produce the analog-to-digital converters (ADC's) capable of digitizingthe signal at the required speed and resolution and (ii) produce aprocessor capable of handling the digitized data at the high speeds.

Therefore, there is a need in the art for an adaptive filtering approachthat combines channel equalization and noise filtering. Another needexists in the art for a method and system for high speed digitalcommunications that combines channel equalization and noise filtering ina single framework and that can account for the effects thatequalization can have on noise filtering, and vice-versa. Additionally,there is a need for such a method and system which is economically andtechnically practical for high-speed data systems.

SUMMARY OF THE INVENTION

A Signal Conditioning Filter (SCF) and a Signal Integrity Unit (SIU) cancontrol elements that filter a digital (i.e. binary or multilevel)signal. A multilevel signal uses discrete amplitudes, which can changefrom one time interval to another, to convey information in each timeinterval. The simplest example of multilevel signaling is binarysignaling where two amplitudes are used to represent a logical 0 or 1(i.e. one bit of information). By using more levels, more informationcan be conveyed with each symbol or in each time interval. In some ofthe prior art and conventional art, the term “multilevel” conveys theuse of more than two amplitude levels. To avoid any ambiguity, the term“digital signaling” will be used in this writing to refer to signalingwith discrete amplitudes and time intervals, i.e. digital signaling thatcan include both binary and multilevel signaling.

The SCF and SIU form part of a method and system for equalizing andfiltering a digital signal. This method and system for equalizing andfiltering may be used in a variety of high-speed communications systems.Applications can include, but are not limited to, (i) electrical systemssuch as backplane, telecom, and datacom systems and (ii) optical systemssuch as long-haul, metro, and short-reach applications.

Regardless of the application, the method and system can process areceived digital signal in the electrical domain prior to decoding.Thus, in optical systems, the method and system can be used either afterphotodetection in the receiver or prior to modulation in thetransmitter.

The present invention can address the coupled problem of equalizationand noise filtering in order to improve signal fidelity for decoding.Specifically, a received digital signal can be filtered in a manner tooptimize the signal fidelity even in the presence of both significant(large magnitudes of) ISI and noise. Furthermore, the method and systemof the present invention can be adaptive in the sense that filtercoefficients can be continuously updated to reflect any time-varyingchanges in the system characteristics.

The present invention can provide an adaptive method that continuouslymonitors a signal fidelity measure. For example, monitoring the fidelityof a digital signal can be performed by external means such as a SignalIntegrity Unit (SIU). A received signal y(t) can be “conditioned” byapplication of a filter with an electronically adjustable impulseresponse g(t). A resulting output z(t) can then be interrogated tocharacterize the quality of the conditioned signal.

This fidelity measure q(t) can then be fed back to the SCF. Utilizingthe signal fed back to the SCF, the response of the SCF can be adjustedto maximize the received fidelity measure. For the SIU, the signalfidelity measure can be directly associated with a decision errorprobability in a subsequent decoder with optimal decision thresholds.Combining the proposed approach with such a control system can balance(in a principled fashion) the trade-off between the degree to which ISIis corrected and noise is mitigated for optimal decoding.

The SCF can include a cascade of two or more tapped delay line filterswith electronically controllable gain coefficients. The tap spacings ofthe two filters can be different in order to effectively combat both theeffect of ISI which occurs on a large time scale and the effects ofnoise, jitter, and signal ringing which occur on a small time scale.

Using a cascade of two distinct filters can minimize the number of tapsrequired to address both of these phenomena. The delay lines in thesefilters can include artificial transmission lines which can absorb theparasitic capacitance of the tap amplifiers. The tap amplifiers whichvary the gain coefficients can be implemented using special Gilbert cellmultipliers.

For one aspect of the present invention, a series of symbols having asymbol period can be processed with filters. A first filter mitigatesdegradation within respective symbols of the series of symbols and asecond filter mitigates inter-symbol interference among the series ofsymbols. The first filter includes delay elements, each having a delayless than the symbol period. The second filter includes delay elementseach having a delay substantially equal to the symbol period. Aprobability estimate can be produced based on an output of at least oneof the first and second filters. A delay for at least one of the delayelements of the first filter or the second filter can be adjustedaccording to the probability estimate.

For another aspect of the present invention, a signal comprising signaldistortions can be processed with filters. The filters comprise a firstfilter configured to a first time scale to compensate for signaldistortions within respective symbols of the signal and a second filterconfigured to a second time scale to compensate for signal distortionsamong symbols of the signal. A probability estimate can be producedbased on an output of at least one of the first and second filters. Atleast one of the first and second time scales is adjusted according tothe probability estimate.

For yet another aspect of the present invention, a digital signal isprocessed to reduce ringing, jitter, or noise within respective symbolsof the digital signal. The digital signal is processed with a firstfilter stage including delay elements each having a first time constantless than a symbol period of the digital signal. Interference betweensymbols of the digital signal is reduced in response to processing thedigital signal with a second filter stage including delay elements eachhaving a second time constant greater than the symbol period. Aprobability estimate can be generated from an output of the first filterstage or the second filter stage. At least one of the first timeconstant and the second time constant can be refined based on theprobability estimate.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates a digital signal receiver architecture according toone exemplary embodiment of the present invention.

FIG. 1B illustrates a signal integrity unit according to one exemplaryembodiment of the present invention.

FIG. 2 illustrates an equalization architecture according to oneexemplary embodiment of the present invention.

FIG. 3 illustrates a short-time filter and a long-time filter that forma signal conditioning filter according to one exemplary embodiment ofthe present invention.

FIG. 4 illustrates a short-time filter in the form of a tapped-delayline filter with small tap delays less than a symbol period of a digitalsignal according to one exemplary embodiment of the present invention.

FIG. 5. illustrates a long-time filter in the form of a tapped-delayline filter with delays substantially equal to the symbol periodaccording to one exemplary embodiment of the present invention.

FIG. 6 illustrates a signal conditioning filter (SCF) forming part of acommunications transmitter according to one exemplary embodiment of thepresent invention.

FIG. 7 is a functional block diagram illustrating a tapped-delay linefilter according to one exemplary embodiment of the present invention.

FIG. 8 is a functional block diagram illustrating a tapped-delay linefilter and one of the exemplary signal paths according to one exemplaryembodiment of the present invention.

FIG. 9 is a functional block diagram illustrating a variable gain tapamplifier according to one exemplary embodiment of the presentinvention.

FIG. 10 is a circuit diagram illustrating a lumped LC delay line thathas terminations provided on either end according to one exemplaryembodiment of the present invention.

FIG. 11 is a circuit diagram illustrating an three-tap tapped-delay linefilter having variable gain amplifiers described in FIG. 18 and delayblocks described in FIG. 19 according to one exemplary embodiment of thepresent invention.

FIG. 12 is a circuit diagram of a variable gain tap amplifier accordingto one exemplary embodiment of the present invention.

FIG. 13 is a circuit diagram of 5-tap tapped-delay line filter withartificial transmission lines according to one exemplary embodiment ofthe present invention.

FIG. 14 is a circuit diagram of an exemplary long-time delay artificialtransmission line according to one exemplary embodiment of the presentinvention.

FIG. 15 is a circuit diagram of an exemplary three-tap tapped-delay linefilter according to one exemplary embodiment of the present invention.

FIG. 16 is a graph that illustrates how the effective Q-factor varieswith the initial iterations of the adaptive filter for an electricalmultilevel signal according to one exemplary embodiment of the presentinvention.

FIG. 17 is a graph that illustrates how the effective Q-factor varieswith the initial iterations of the adaptive filter for a multilevelsignal going through 100 km of fiber according to one exemplaryembodiment of the present invention.

FIG. 18 is a graph of an Eye-diagram for an unfiltered multilevelelectrical drive signal that can be used as an input to the presentinvention.

FIG. 19 is a graph of an Eye-diagram for a filtered multilevelelectrical drive signal according to one exemplary embodiment of thepresent invention.

FIG. 20 is a graph of an Eye-diagram for an unfiltered multileveloptical signal that can be used as an input to the present invention.

FIG. 21 is a graph of an Eye-diagram for a filtered multilevel opticalsignal according to one exemplary embodiment of the present invention.

FIG. 22 is a graph illustrating how the effective Q-factor varies withthe initial iterations of the adaptive filter for a multilevel signalwith inter-symbol interference according to one exemplary embodiment ofthe present invention.

FIG. 23 is a graph of an Eye-diagram for an unfiltered multileveloptical signal that can be used as an input to the present invention.

FIG. 24 is a graph of an Eye-diagram for a filtered multilevel opticalsignal according to one exemplary embodiment of the present invention.

FIG. 25 illustrates a signal conditioning filter (SCF) fabricated inGaAs as an integrated circuit that contains a variable gain inputamplifier and a transit detector circuit for clock recovery according toone exemplary embodiment of the present invention.

FIG. 26 is a graph that illustrates a 5 Gbps unfiltered binary signalafter transmission over 34″ of copper trace in a backplane that can usedas input to the present invention.

FIG. 27 is a graph that illustrates the signal of FIG. 26 afterequalization with the signal conditioning filter according to oneexemplary embodiment of the present invention.

FIG. 28 is a graph that illustrates an unfiltered 10 Gbps (4-level 5 Gsym/s) signal after transmission over 150 m of multimode fiber that canbe used as input to the present invention.

FIG. 29 is a graph that illustrates the multilevel signal of FIG. 28after equalization with the signal conditioning filter according to oneexemplary embodiment of the present invention.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

The present invention can address the problems of equalization and noisefiltering in order to improve signal fidelity for decoding.Specifically, a received digital signal can be filtered in a manner tooptimize the signal fidelity even in the presence of both largemagnitudes of ISI and noise. Furthermore, the method and system of thepresent invention can be adaptive in the sense that filter coefficientscan be continuously updated to reflect any time-varying changes in thechannel behavior.

Filter Structure

Referring now to FIG. 1A, an equalization and filtering system 102 cancomprise a variable gain amplifier 105, a signal conditioning filter(SCF) 100, a decoder or clock and data recovery (CDR) unit 120, and asignal integrity unit (SIU) 125. The CDR 120, SIU 125, and VGA 105 canform parts of a signal detection and fidelity characterization circuit130 as will be discussed below with respect to FIG. 2. The exemplarysignal conditioning filter (SCF) 100 can comprise two filters, ashort-time filter 110 and a long-time filter 115 that are cascadedtogether.

According to one exemplary embodiment, each filter 110, 115 of thesignal conditioning filter 100 can comprise a tapped-delay line orfinite impulse response (FIR) filter with electrically controllable gaincoefficients. Filtering is separated into these two stages, where theshort-time filter 110 can comprise the first stage and the long-timefilter can comprise the second stage. Each stage is designed to addressa particular type of distortion using a relatively small number of taps.

As its name implies, the short-time filter 110 can be designed tomitigate degradations such as ringing, noise, and timing jitter that canoccur on a relatively small time scale. Meanwhile, the long-time filter115 is designed to remove signal artifacts (such as ISI) that can occuron a larger time scale.

Referring now to FIG. 1B, the signal integrity unit 125 can comprise alow pass filter (LPF) 132 and an analog-to-digital converter 135, acontroller or processor 140, and a plurality of digital-to-analogconverters (DACs) 145. After low-pass filtering by the LPF 132, a DCcomponent of the sampled signal remains and is termed the event monitorvoltage and is an analog probability estimate for the controlledreference voltage exceeding the received signal y(t) where controlledreference voltage is generated by the digital-to-analog converters 145.

As mentioned above, the output of the LPF 132 can be fed to theanalog-to-digital converter (ADC) 135. The ADC 135 may be characterizedas a low-speed high-resolution ADC that measures the averagedevent-detector output representing the cumulative distribution function(CDF) value. Specifically, the reference voltage is swept over a rangeof voltage levels while the ADC 135 samples the voltage from the filter132 to produce an estimate of the CDF. The SIU 125 can set the referencevoltage via the DAC 145 to a fixed value and then measures the averagedevent detection output. The SIU 125 can then set the reference voltageto a different fixed value and measures another point of the CDF. Thisprocess is completed until the CDF curve is formed.

The ADC 135 feeds its output to a microcontroller 140. Microcontroller140 can process the cumulative distribution function (CDF) to determinethreshold voltage values for signal decoding, receiver gain for thevariable gain amplifier 105, and filter coefficients for the SCF 100.The microcontroller 140 is responsible for feeding the filtercoefficients to the SCF for equalizing and filtering the receivedsignal. Further details of the signal integrity unit 125 are discussedin the commonly owned U.S. Non-provisional application Ser. No.10/108,598 entitled, “METHOD AND SYSTEM FOR DECODING MULTILEVELSIGNALS,” filed on Mar. 28, 2002 in the name of Vincent Hietala et al.,the entire contents of which are hereby incorporated by reference.

Referring now to FIG. 2, a first input to the signal conditioning filter(SCF) 100 can comprise a signal y(t) that can include an unfilteredreceived signal while the output to the SCF 100 can comprise a filteredsignal z(t). The filtered signal z(t) can be propagated into the signaldetection and fidelity characterization circuit 130. As mentioned above,the signal detection and fidelity characterization circuit 130 cancomprise a CDR 120 and SIU 125.

A first output of the signal detection and fidelity characterizationcircuit 130 can comprise the decoded data from the filtered signal z(t).A second output of the signal detection and fidelity characterizationcircuit 130 can comprise a control signal q(t) that forms a second inputto the SCF 100.

Referring now to FIG. 3, as noted above with respect to FIG. 1, the SCF100 can comprise a short-time filter 110 that receives the signal y(t)discussed above with respect to FIG. 2. The short-time filter 110manipulates the signal y(t) according to a first function g_(S)(t). Theoutput from the short-time filter 110 can comprise a first filteredsignal y-prime′(t) that is fed as the input to the long-time filter 115.

The long-time filter 115 manipulates the signal y-prime′(t) according toa second function g_(L)(t). The output from the long-time filter 115 cancomprise a second filtered signal or z(t) as mentioned above withrespect to FIG. 2 that is fed as the input to the CDR 120 or SIU 125(not shown in FIG. 2).

Referring now to FIG. 4, the exemplary short-time filter 110 cancomprise a tapped-delay line filter with amplifiers 405 and N delayelements 410 (each with delay δ) and N+1 amplifiers with gaincoefficients α_(n) for n=0, . . . , N. The delay δ can be chosen to besmall (relative to the symbol period T₀ of the signal) to permit theshort-time filter 110 to perform at least one of three functions: (1)compensate for signal distortions (such as ringing) that can occurwithin a single symbol period; (2) effectively integrate over less thana symbol period to integrate out and reduce the noise; and (3) adjustthe amount of signal smoothing to be large enough to reduce the effectsof signal distortion and noise but to be short enough to be robustrelative to the timing jitter in the system.

The short-time filter 110 can support a frequency resolution of 1/Nδ. Itis assumed that the delay δ is sufficiently small so that there is noaliasing in the short-time filter 110. Specifically, the short-timefilter 110 has a frequency response that is periodic in frequency withperiod 1/δ. Any signal (or noise) energy at frequencies higher thanf=1/(2δ) will distort the filtered signal as they overlap into adjacentspectral periods. Because of this distortion, it is recommended that thesignal be pre-filtered with a passive analog low-pass filter (not shown)prior to the short-time filter 110. This pre-filtering may not be neededif any of the receiver components already sufficiently bandlimits thesignal, as is often the case with circuit hardware and the high speedsconsidered.

The output of the short-time filter 110 can be written asy′(t)=α₀ y(t)+α₁ y(t−δ)+ . . . +α_(N) y(t−Nδ)  (1)or equivalently asy′(t)=[α₀+α₁+ . . . +α_(N) ]y(t)−α₁ [y(t)−y(t−δ)]− . . . −α_(N)[y(t)−y(t−Nδ)]  (2)where the latter form explicitly conveys how the short-time filter 110operates on the difference between the current sample and a sample fromthe past, i.e. each term can provide a first-order correction for thesignal fluctuation within a symbol period. Furthermore, the coefficienton y(t) in Eq. (2) provides the DC gain of the signal, i.e. the gain onthe signal when the signal is already flat within a symbol period, andhence, all the differential terms are zero. As a reference, unity DCgain can be chosen by setting α₀ toα₀=1−α₁− . . . −α_(N)  (3)or by alternatively normalizing the filter coefficients to sum to one.

Referring now to FIG. 5, the exemplary long-time filter 115 can comprisea tapped-delay line filter with M delay elements 410′ (each with a delayequal to the symbol period T₀) and M+1 amplifiers 405 with gaincoefficients a_(m) for m=0, . . . , M. The purpose of this long-timefilter 115 is to remove ISI which occurs between symbols. Because theshort-time filter 110 is capable of smoothing the signal over asignificant portion of the symbol period, the long-time filter 115 neednot worry about aliasing associated with the signal frequencies higherthan the sampling rate 1/T₀. If the short-time filter 115 were notpresent, then an anti-aliasing filter with a low-cutoff frequency may beneeded.

Similar to Eqs. (1) and (2), the output of the long-time filter 115 canbe written asz(t)=a ₀ y′(t)+a ₁ y′(t−T ₀)+ . . . +a _(M) y′(t−MT ₀)  (4)or equivalently,z(t)=[a ₀ +a ₁ + . . . +a _(M) ]y′(t)−a ₁ [y′(t)−y′(t−Δ)]− . . . −a _(M)[y′(t)−y′(t−MΔ)]  (5)where again, a unity DC gain can be arbitrarily chosen by settinga ₀=1−a ₁ − . . . −a _(N)  (6)or by scaling the coefficients to sum to one.

Those skilled in the art can extend the exemplary filters in FIGS. 4 and5 to account for subsequent as well as preceding signal samples. Forexample, additional L taps could be added to the short-time filter 110of FIG. 4 to change Eq. (2) to yieldy′(t)=[α₀+ . . . +α_(N+L) ]y(t)−α₁ [y(t)−y(t−δ)]− . . . −α_(N+L)[y(t)−y(t−(N+L)δ)].The signal sample y(t−Lδ) can be interpreted as the sample to bedecoded, i.e. where the decoding has been delayed by process by time Lδ.Because, the signal points y(t) through y(t−(L−1)δ) precede y(t−Lδ), theISI associated from these symbols can be removed. Thus, the short-timefilter 110 can now remove ISI originating from both preceding andsucceeding signal samples. The long-time filter 115 may be similarlymodified. This extension can be applied to both the short and long-timefilters 110, 115 in practice as it can help improve equalization.Filtering in the Transmitter

Referring now to FIG. 6, although described for use in a receiver, theSCF 110 may also be used in a transmitter 600 to maximize the fidelityof the transmit signal before channel noise is introduced which limitssignal restoration in a corresponding receiver (not shown).Specifically, SCF 100 and SIU 125 modules may be placed in thetransmitter 600 immediately before transmission circuitry as illustratedin FIG. 6 where these modules can be used to minimize the effects ofringing, ISI, circuit impedance mismatches, and noise introduced by thetransmitter.

Removing these distortions prior to transmission is advantageous becausethe noise introduced by the channel limits the degree to which thetransmitter 600 distortions can be compensated by the receiver's SCF100. Additionally, if a supervisory communications link is availablebetween the transmitter 600 and receiver (not shown), then the fidelitysignal q(t) may be fed from the receiver (not shown) to the transmitter600 over this link so that the SCF 100 in the transmitter not onlycompensates for transmitter distortions, but also pre-compensates forlink distortions. This pre-compensation would be advantageous because itprevents the noise introduced by the link from limiting the degree towhich the channel distortions can be compensated.

Filter Realization

The exemplary short- and long-time filters 110, 115 forming the SCF 100can be implemented using an integrated tapped-delay line filterstructure 100A with the basic structure illustrated in FIG. 7. Thisexemplary filter structure 100A is functionally identical to theconceptual tapped-delay line filter diagrams of FIGS. 3 and 4 if τ isassociated with δ for FIG. 4 and T₀ for FIG. 5.

The filter structure 100A shown in FIG. 7 offers efficient “re-use” ofthe time delays for the various signal paths. This can be importantsince time delays are generally physically quite large and thusdifficult to integrate. Therefore, it is desirable to make optimal useof all delay elements.

To understand this efficient “re-use” of the delays, shown in FIG. 8 isthe signal path for the third filter tap with gain coefficient g3. Forthis tap, by inspection, the total signal delay will be six times (×)τ/2 or 3τ. Similarly, by observation, the delay of the signal for eachtap g_(i) is i (times)×τ. Thus, the output signal y(t) can berepresented as follows:

$\begin{matrix}{{{y(t)} = {\sum\limits_{k = 0}^{4}{g_{k}{x\left( {t - {k\;\tau}} \right)}}}},} & (7)\end{matrix}$which is identical to the form of Equations (1) and (4) discussed above.

A block diagram of an exemplary variable gain tap amplifier 900 for atap filter is illustrated in FIG. 9. In this exemplary embodiment, thegain constant GC is multiplied with the signal Vin to allow for bothpositive and negative gain coefficients. The input signal Vin isamplified/buffered, multiplied by the gain coefficient GC, and thenoutput as a current source Iout. The input amplifier/buffer 902 isdesigned to have high input impedance as to not disturb the input delayline. The output of the amplifier 900 is also designed to be highimpedance as to similarly not disturb the output delay line. Inpractice, a significant parasitic capacitance remains at both the inputand output of the amplifier 900, but as will be seen below, theseparasitics can be absorbed into the delay lines.

For one exemplary embodiment of the present invention, a delay elementcan comprise a simple LC (inductor-capacitor) delay line. However, thoseskilled in art will recognize that other delay elements can be used andare not beyond the scope and spirit of the present invention.

A representative LC delay line 1800 is illustrated in FIG. 10. Thisdelay line 1000 forms a high order low-pass filter function with arelatively constant delay over the passband. Those skilled-in-the-artwill recognize that a variety of filter design methodologies could beemployed to construct higher performance delay structures, but the oneshown in FIG. 10 was used for simplicity. It should also be realizedthat the lumped elements could be realized by distributed elements or infact a variety of different delay elements could be similarly used.

For the simple delay structure shown, assuming constant L and C_(l), thedelay, τ is approximately:τ≈N _(LC) √{square root over (LC_(l))}  (8)in which N_(LC) is the number of LC pairs and the filter's terminationresistance, R_(o) is:

$\begin{matrix}{R_{o} \approx \sqrt{\frac{L}{C_{l}}}} & (9)\end{matrix}$The end of each delay element needs to be terminated with R_(o) inparallel with a capacitor of approximately C_(l)/2 for proper operation.

Referring now to FIG. 11, an exemplary embodiment of a three taptapped-delay line filter 100C using the variable gain tap amplifier ofFIG. 9 and the lumped LC delay element shown in FIG. 10 is illustrated.Several important design aspects of this filter structure 100C can nowbe explained.

First, it is important to realize that the cascade of delay elements1102 and circuitry on the left-hand side of the circuit 100C is designedto form a well controlled delay line. This will be referred to as the“input delay line” 1102. Similarly, on the right-hand side of thecircuit 100C comprising the two delay elements and associated circuitryin this simple exemplary embodiment, will be referred to as the “outputdelay line” 1104.

Both the input and output delay lines 1102, 1104 are designed to haveminimal signal attenuation and reflections in order to maintain goodsignal fidelity. As such, as already mentioned, the inputs of theamplifiers g were designed with high impedance and the remaining inputcapacitance is “absorbed” into the loading capacitance of the inputdelay line 1102.

This absorbed capacitance can be seen in FIG. 11 by the reduced valuesof loading capacitance (C_(l)−C_(in)). Additionally, the input and theoutput of the input delay lines 1102, 1104 are carefully terminated inthe characteristic resistance (R_(o)) of the delay elements. Similarly,the output delay line 1104 absorbs the output parasitic capacitance ofthe amplifiers and is terminated with the appropriate resistance(R_(o)). The output of each amplifier g launches a signal in bothdirections in the output delay line 1104 and thus it can be appreciatedwhy proper termination can be critical for proper filter operation.

FIGS. 12 through 15 illustrate an exemplary circuit embodiment of twotap tapped-delay line filters. The designs are fully differential, butone skilled-in-the-art will realize that the concepts discussed aboveare equally applicable to differential or single-ended designs. Theparticular exemplary embodiments illustrated in these figures are forintegration in a GaAs HBT process. One skilled-in-the-art will realizethat other device technologies could similarly be applied.

Specifically, FIG. 12 illustrates the circuit diagram of an exemplaryvariable gain tap amplifier 1200. The input is first buffered by highinput-impedance emitter follower amplifiers X16 and X17. The output ofthe emitter follower amplifiers drives a lower pair of a standardGilbert cell multiplier circuit (also called a Gilbert cell mixer and anXOR gate) comprising X14, X13, X9, X10, X11 and X12. The bases of theupper cross connected differential pairs are held at the desired DC gainconstant. Since this circuit is an effect 4-quadrant multiplier, thegain coefficient can be negative or positive.

The R8, R10 and R9, R11 resistor divider networks scale the input drivevoltage so that desired coefficient control range is achieved (approx.+/−1 V in this case). The output of the Gilbert cell multiplier circuitis terminated by the output delay line. The Gilbert cell multiplier willusually see a real load resistance of R_(o)/2. The output will have asignificant output capacitance due the collector capacitances of X9,X10, X11, and X12, but as discussed above, this capacitance can beabsorbed into the output delay line.

Referring now to FIG. 13, the design for an exemplary 5-tap τ=T₀/5short-time tapped-delay line filter 100D that is based on artificialtransmission lines is illustrated. For this filter 100D, it was foundthat only one LC pair was required for each tap (2^(nd) order low-passfilter). Each delay element can provide 37 (pico-seconds) ps of delay (½of ⅕ period at 2.7 Gbps). The inductors used were integrated spiralinductors with a nominal inductance of 2.7 nH. The actual loadingcapacitor values were initially selected as indicated above, butoptimized for the best frequency response in the actual design. A seriesresistance R1304 was added to the loading capacitors C1304 to lower thephase peaking at the stopband edge. An additional shunt resistance R1306was added to help counteract the effect of the inductor loss Inductorloss makes the delay lines characteristic resistance complex. Theaddition of an appropriate shunt resistance can cancel this effect andmake the characteristic impedance real at a target frequency. The inputand output of the filter 100D are buffered by amplifiers 1302 to isolatethe circuit from external influences.

For the long-time filter 115 (3-tap τ=T₀), a six stage LC filter wasrequired to obtain the necessary delay of 185 ps. Referring now to FIG.14, this figure illustrates an exemplary circuit of an individual longdelay element 1400. Four of these long delay elements 1400 were used inthe exemplary filter embodiment 100E illustrated in FIG. 15. Theexemplary filter embodiment 100E of FIG. 15 can be referred to as a3-tap long-time tapped-delay line filter.

Coefficient Adaptation Algorithm

The gains of the filter tap amplifiers g are adjusted to maximize asignal fidelity measure q(t) (provided by the SIU 125 for example). Thegeneral idea is to slightly perturb the coefficients and observe theeffect on q(t). Doing this allows a set of coefficient values to bedetermined that locally maximizes the signal fidelity. The approachcontinually perturbs the coefficients to survey the signal fidelity'sdependence on the coefficients and tune the SCF 100 to the optimalvalues in an adaptive fashion. The method is presented for the case ofthe short-time filter, but the approach is equally applicable to thelong-time filter. Alternatively, the cascade of the two filters can beviewed as a single filter whose coefficients are adapted by thefollowing method as will be discussed below.

The intuition in the preceding paragraph can be made precise byrestating it as the following optimization problem

$\begin{matrix}{\alpha^{*} = {\underset{\alpha}{\arg\;\max}\left\{ {q(t)} \right\}}} & (10)\end{matrix}$where α denotes the vector of adjustable filter coefficients and q(t)quantifies the fidelity of the signal (such as a measure of the signal'sQ-factor as produced by the SIU[4]). Eq. (10) is solved via an empiricalminimization of q(t). Towards this end, a coordinate descent algorithmcan be used to find the local maximum by searching over each coordinatewhile the others are held fixed (i.e. perturbing one of the filtercoefficients α₀, α₁, . . . , α_(N) at a time). One skilled in the artwill realize that other numerical optimization techniques (such asgradient, Newton, and conjugate methods) may also be used to solve Eq.(10).

In some contexts, simply maximizing the signal fidelity may not besufficient to provide good SCF performance. In particular, there is thepossibility of a null-space of solutions. For example, consider the taskof short-time equalization when there is no ringing and noise on thereceived signal to compensate. An intuitive solution would be to haveα₀=1 and α_(n)=0 for all other n, i.e. perform no filtering. However, anequally valid solution would be, α₀=1, α₁=A, α₂=−A, and α_(n)=0 for allother n where A can be any value (including arbitrarily large values).Other convoluted (but still valid) sets of coefficients can also beobtained. The drawbacks of such non-intuitive solutions are

-   1. They obscure the identifiability of the coefficients which are    actually helping to improve signal fidelity. For instance, in the    above example, α₁ and α₂ effectively cancel each other and do    nothing to reduce ringing or noise.-   2. They reduce the robustness of the system to changes in the    channel characteristics. In particular, if the channel    characteristics change such that the null-space “moves” (e.g. a    little ringing is introduced), then α₁ and α₂ will no longer cancel    each other and a very erratic signal will result until the    coefficients are relearned to remove such artifacts.

Motivated by such problems, there may be the desire to guide the valuesof the filter coefficients α_(n), in addition to maximizing the signalfidelity. To achieve such a result, a regularization penalty can beimposed in the objective function. For example, solving the followingoptimization problem could be chosen in place of Eq. (10):

$\begin{matrix}{\alpha^{*} = {\underset{\alpha}{\arg\;\max}\left\{ {{q(t)}^{2} - {\gamma{{\alpha - \beta}}_{2}^{2}}} \right\}}} & (11)\end{matrix}$where γ and β are regularization parameters. The parameter β is anominal value for α. Specifically, β is the value one would expect α* tobe in the absence of any channel distortion. While β represents thenominal value of α*, γ represents confidence in β and determines howstrongly α* is driven towards β. Note that if no biasing is desired,then γ should be set to zero, and Eq. (11) reduces to Eq. (10). Thus,Eq. (10) can be seen as a specific case of Eq. (11). One skilled in theart will realize that a variety of penalty functions can be used inplace of the 2-norm in Eq. (11).

As previously stated, the long-time filter coefficients can similarly beadapted according to Eq. (11), i.e. it can be chosen that

$\begin{matrix}{a^{*} = {\underset{a}{\arg\;\max}\left\{ {{q(t)}^{2} - {\gamma{{a - b}}_{2}^{2}}} \right\}}} & (12)\end{matrix}$where b is the nominal value for the long-time filter coefficients. Thenominal situation again corresponds to when the channel introduces nosignal distortion. For example, if one generally believes the channelintroduces no ISI, then b should generally resemble a Euclidean basisvector, i.e. a vector with a single 1 and the rest zeros. That is, thenominal long-time filter should not do much filtering.Automatic Gain Control

Thus far, the special case of no DC amplification on the filteredmultilevel signal has been considered. A non-unity gain could beselected. And if a variable gain amplifier (VGA) module 105 is to leador follow the SCF 100, then the control of the VGA module 105 may beincorporated into the SCF's 100 control. In particular, if the desiredgain A_(VGA) can be obtained as an external signal (perhaps determinedin the SIU 125, then the SCF 100 can control the gain by simply scalingall of the coefficients α_(n) (or a_(n)) by A_(VGA). This is simply amathematical operation that can be performed after the calculation offilter coefficients in Eq. (11) or (12). Alternately, the gain controlof the VGA module 105 can be adjusted as needed by the SIU.

Simulation Results

To demonstrate results of the proposed filtering method, the inventorscompleted a MATLAB simulation as applied to real data of a 4-PAM signalin an optical communications system.

First, a system dominated by short-time effects, i.e. ringing and noise,is examined. Specifically, an electrical drive signal and a receivedsignal after 100 km of fiber is considered. The progression of thefidelity measure as the filter adaptation algorithm iterates is shown inFIG. 16 (for the electrical drive signal) and 17 (for the receivedoptical signal). Specifically, the graph 1600 in FIG. 16 conveys thevalue of the signal fidelity measure as the filter coefficients arebeing adjusted. From the plot 1602, it can be seen that the fidelity ofthe signal is improved as the coefficients are adjusted. The numericalimprovement conveyed by plot 1602 can be further appreciated byconsidering the eye-diagrams in FIGS. 18 and 19. FIG. 18 shows the eyediagram for the signal before any filtering, i.e. at iteration 0 ingraph 1600. FIG. 19 shows the eye-diagram of the signal after filteringon iteration 7 in graph 1600. Clearly, the amount of ringing on thesignal has been reduced through the use of filtering providing a betterquality signal.

FIG. 17 is analogous to FIG. 16, except that FIG. 17 is for aphotodetected optical signal after 100 km of optical fiber.Specifically, graph 1700 in FIG. 17 shows the progression of thefidelity measure as the filter coefficients are adjusted in eachiteration for this optical system. FIGS. 20 and 21 are analogous toFIGS. 18 and 19. In particular, FIG. 20 shows an eye-diagram of thephotodetected optical signal before any filtering. Clearly, the signalis of poor quality as exhibited by the nearly closed eye-openings 2002C.FIG. 21, however, shows very wide eye-openings 2002D that are producedafter filtering the signal with the described invention.

In addition to the short-time distortion noise dominated data sets inFIGS. 16 through 22, another data set in which the signal ispredominantly degraded by ISI is examined. Again, the context is anoptical system with 100 km of fiber, but contrary to the system used forFIGS. 8, 11, and 12, a different photodetector is used which is lessvulnerable to noise, thus leaving ISI as the dominant source of signaldegradation. The evolution of the signal fidelity is shown in FIG. 22from which we see a significant improvement in signal quality (almostdoubling the fidelity measure). The eye-diagrams associated with the SCFare shown in FIG. 23 (without filtering) and 24 (with filtering). Theincrease in the eye-opening from before filtering 2302A to afterfiltering 2302B clearly conveys the improvement in signal qualityafforded by the SCF.

Laboratory Results

An exemplary IC implements the filter embodiment discussed above, asillustrated by the circuit 2500 of FIG. 25. The circuit 2500 wasfabricated in a GaAs HBT process. The short-time filter 2505 comprisesfive coefficient amplifiers 2510 and eight delay elements 2515 torealize the 5-tap tapped-delay line filter illustrated in FIG. 22. Aspreviously described, a pair of τ/2 delay elements 2515 are used toproduce the desired delay of τ (τ/2 from the input side and τ/2 from theoutput side).

Meanwhile, the long-time filter 2520 comprises three coefficientamplifiers 2510 and four delay elements 2525 to realize the 3-taplong-time filter illustrated in FIG. 24. Coefficient amplifiers 2510 areGilbert cell multipliers with identical topologies, although specificcircuit parameters may vary as each multiplier is optimized according tothe surrounding circuit.

The improved output provided by the SCF circuit 2500 of FIG. 25 isillustrated by FIGS. 26 and 27. FIG. 26 illustrates a received signalfrom a backplane communications system transmitting a binary signal at adata rate of 5 Gbps over a 34″ copper trace. Specifically, FIG. 26illustrates the condition of the received electrical binary signal inthe form of an eye-diagram 2600. Clearly, no reliable data can berecovered from this received signal as there is no eye-opening.

Meanwhile, referring now to FIG. 27, this figure shows an eye-diagram2700 for the same received signal illustrated in FIG. 26 but beingprocessed by the SCF 100 and its corresponding control method. Theeye-openings 2705 are now clearly visible affording reliablecommunications which was unachievable without equalization.

Referring now to FIGS. 28 and 29, these figures demonstrate theimprovement provided by the SCF 100 in an optical communications system.The system channel now includes optical components. Specifically, theelectrical data signal is converted to an optical signal with a VCSEL(vertical cavity surface emitting laser), transmitted over 150 m ofmultimode fiber (MMF), and converted back to an electrical signal at thereceiver with a photodetector.

FIG. 28 illustrates an eye diagram 2800 where the condition of thereceived electrical signal when a 4-level 5 Gsym/s (yielding a 10 Gbpsdata rate) is transmitted. Again, there are no visible eye-openings inthe received signal and thus data cannot be reliably recovered.

Meanwhile, in FIG. 29, an eye-diagram 2900 for the same received signalis illustrated but after filtering with the SCF 100 of one exemplaryembodiment of the present invention. The four signal levels are nowapparent from the eye-openings 2905 which means that data can berecovered from this received and filtered signal.

Therefore, the present invention provides an adaptive filtering approachthat combines channel equalization and noise filtering. The method andsystem of the present invention can easily support high speed digitalcommunications which combines channel equalization and noise filteringin a single framework. The method and system of the present inventioncan account for the effects that equalization can have on noisefiltering, and vice-versa. Furthermore, the method and system areadaptive in nature and have a practical means of implementation forhigh-speed data communications systems.

It should be understood that the foregoing relates only to illustratethe embodiments of the present invention, and that numerous changes maybe made therein without departing from the scope and spirit of theinvention as defined by the following claims.

The invention claimed is:
 1. A method for processing a series of symbolshaving a symbol period, comprising: mitigating, by a first filter,degradation within respective symbols of the series of symbols, thefirst filter including a first plurality of delay elements each having adelay less than the symbol period; mitigating, by a second filter,inter-symbol interference among the series of symbols, the second filterincluding a second plurality of delay elements each having a delaysubstantially equal to the symbol period; producing a probabilityestimate based on an output of at least one of the first and secondfilters; and adjusting a delay of at least one of the delay elements ofthe first and second plurality of delay elements according to theprobability estimate.
 2. The method of claim 1, wherein the first filtercomprises a first analog filter and the second filter comprises a secondanalog filter.
 3. The method of claim 1, wherein the probabilityestimate comprises an analog probability estimate.
 4. The method ofclaim 1, wherein the adjusting comprises adjusting, according to theprobability estimate, a first time scale of the first filter and asecond time scale of the second filter.
 5. The method of claim 1,wherein the degradation within respective symbols of the series ofsymbols comprises ringing.
 6. The method of claim 1, wherein the firstfilter comprises a first linear tapped-delay line filter and the secondfilter comprises a second a linear tapped-delay line filter.
 7. Themethod of claim 1, wherein the symbol period specifies a time intervalspanning between two temporally adjacent symbols in the series ofsymbols.
 8. The method of claim 1, wherein the series of symbolscomprises a communication signal.
 9. A method for processing a digitalsignal, comprising: reducing ringing, jitter, or noise within respectivesymbols of the digital signal in response to processing the digitalsignal with a first filter stage including delay elements each having afirst time constant less than a symbol period of the digital signal;reducing interference between symbols of the digital signal in responseto processing the digital signal with a second filter stage includingdelay elements each having a second time constant greater than thesymbol period; generating a probability estimate from an output of thefirst filter stage or the second filter stage; and refining at least oneof the first time constant and the second time constant based on theprobability estimate.
 10. The method of claim 9, wherein the firstfilter stage feeds the second filter stage and the generating comprisesgenerating the probability estimate from an output of the second filterstage.
 11. The method of claim 9, wherein the second time constant isgreater than the first time constant.
 12. The method of claim 9, whereinthe symbol period specifies a time interval spanning between twotemporally adjacent symbols in a series of symbols of the digitalsignal.
 13. The method of claim 9, wherein at least one of the first andsecond filters comprises a Gilbert cell coefficient multiplier.